In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive pro…
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48 results for “Successive Nonnegative Projection Algorithm”
A new NMF variant tackles underdetermined problems with sparse and separable assumptions.
problem Underdetermined blind source separation, especially multispectral image unmixing.
method Sparse Separable Nonnegative Matrix Factorization (SSNMF) combining separability and sparsity assumptions. Algorithm based on SNPA and sparse nonnegative least squares.
result In noiseless settings, the algorithm recovers true underlying sources.
The successive projection algorithm (SPA) is a fast algorithm to tackle separable nonnegative matrix factorization (NMF). Given a nonnegative data matrix , SPA identifies an index set such that there exists a nonnegative matrix with . SPA has been successfully used as a…
New algorithms SVCA and SSPA improve robustness to noise in nonnegative matrix factorization.
problem Estimating vertices from noisy data points in convex hull.
method Smoothed VCA (SVCA) and Smoothed SPA (SSPA) algorithms.
result Improved robustness to noise compared to existing methods.
The successive projection algorithm (SPA) has been known to work well for separable nonnegative matrix factorization (NMF) problems arising in applications, such as topic extraction from documents and endmember detection in hyperspectral images. One of the reasons is in that the algorithm is robust to noise. Gillis and…
New algorithms improve blind source separation for linear-quadratic mixtures.
problem Blind source separation of linear-quadratic mixtures under separability assumptions.
method Proposed two algorithms: SNPALQ and BF. SNPALQ generalizes SNPA for LQ model, BF post-processes SNPALQ.
result Proven robustness and computational tractability of SNPALQ in separating sources even with noise.
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing. This problem is referred to as near-separable NMF and requires that there exist…
Nonnegative low-rank matrix recovery can have spurious local minima.
problem Nonnegative low-rank matrix recovery problems can have spurious local minima.
method Investigated projected gradient methods for nonnegative low-rank recovery problems.
result Benign nonconvexity holds in the fully-observed case with RIP constant δ=0 but fails in the partially-observed case and higher-rank ground truths.
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix and a factorization rank , NMF looks for a nonnegative matrix with columns and a …
New method reduces computational cost for nonnegative low rank matrix approximation.
problem Efficiently compute nonnegative low rank matrix approximation for nonnegative matrices.
method Alternating projections onto tangent spaces of fixed rank matrices manifold and nonnegative matrix manifold.
result Sequence converges linearly to optimal solutions, showing better performance in terms of computational time and accuracy.
Proposes TS-NMF for 2D clustering, preserving spatial info.
problem Loss of spatial information in 2D data.
method Semi-Nonnegative Matrix Factorization with manifold learning.
result Improves clustering performance compared to state-of-the-art.
On the structure of compact Kähler manifolds with nonnegative holomorphic sectional curvaturemath.DG
The paper proves properties of complex manifolds with nonnegative holomorphic sectional curvature.
problem Characterizing compact Kähler manifolds with nonnegative holomorphic sectional curvature.
method Holonomy principle and geometric properties.
result Compact Kähler manifolds with nonnegative holomorphic sectional curvature are projective and rationally connected.
The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise are small. In particular, robustness against noise should be high when handling th…
Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint, whic…
This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states is characterized by the nonnegative rank of the Markov transition mat…
We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain nonnegatively curved manifolds. The procedure yields new metrics of nonnegative sect…
New method sets explicit sparsity for groups of vectors in deep learning and NMF.
problem Tackles the challenge of achieving a desired average sparsity level in vector groups.
method Designs a new sparse projection method that sets the sparsity level for the whole set explicitly and automatically tunes the sparsity of each vector.
result Shows significant improvements in accuracy and reconstruction errors compared to existing methods in deep learning and NMF.
The study shows conditions for Kähler manifolds to have rational cohomology of complex projective space.
problem Conditions for Kähler manifolds to have rational cohomology of complex projective space.
method Analyzing the Calabi curvature operator and its positivity conditions.
result Compact Kähler manifolds with specific curvature conditions have rational cohomology of complex projective space.
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that they are closely linked. In this report, we provide a gentle introduction to clu…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor to this is the increasingly growing size of the datasets available and needed in …
We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We prove that the sequence of learned dictionaries converges almost surely to the set…
Paper improves SPA and its variants' robustness to noise.
problem Robustness of successive projection algorithm (SPA) and its variants to noise.
method Proved and improved error bounds for SPA and variants.
result Significantly improved error bounds for SPA and variants under specific conditions.
Defines projective Ricci curvature and proves rigidity for sprays.
problem Defining and studying projective Ricci curvature.
method Introduced projective Ricci-flat sprays and studied Randers metrics.
result Global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature.
This paper defines RII number for knot projections and shows it can be any nonnegative number.
problem Defining and quantifying the minimum number of specific types of deformations for knot projections.
method Using deformations of types 1, 2, and 3, analogs of Reidemeister moves, to simplify knot projections and define RII number.
result RII number can be any nonnegative number, not just zero as previously conjectured.
For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is a nontrivial complex line bundle ove…
Paper proposes a clustering algorithm for nonnegative data.
problem Clustering nonnegative data in disjoint subspaces.
method Simple algorithm to cluster nonnegative data.
result Matrix completion algorithm outperforms standard methods.
The key condition A3w of Ma, Trudinger and Wang for regularity of optimal transportation maps is implied by the nonnegativity of a pseudo-Riemannian curvature -- which we call cross-curvature -- induced by the transportation cost. For the Riemannian distance squared cost, it is shown that (1) cross-curvature nonnegativ…
Paper proposes ONTD for nonnegative tensor data.
problem Handling nonnegative tensor data efficiently.
method Orthogonal Nonnegative Tucker Decomposition (ONTD) with convex relaxation algorithm.
result Demonstrates effectiveness on real-world image data applications.
In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization algorithms. Our analysis focuses on the successive projection algorithm (SPA), …
New PSDMF algorithms derived from PR and ARM methods.
problem Positive semidefinite matrix factorization (PSDMF) challenges.
method Design PSDMF algorithms based on phase retrieval (PR) and affine rank minimization (ARM) methods.
result New PSDMF algorithms inherit numerical properties from PR and ARM methods.
Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descentstat.ML
Develops first and second-order pseudo-mirror descent methods for nonnegative function estimation.
problem Nonnegative function estimation in settings like MLE and trajectory optimization.
method First and second-order pseudo-mirror descent with pseudo-gradients and projections.
result Establishes tradeoffs and non-asymptotic bounds on model complexity.
New NMF algorithm uses Toeplitz matrix for facial recognition.
problem Facial recognition performance improvement.
method Proposes TNMF algorithm with Toeplitz penalty for NMF.
result TNMF outperforms ZNMF and other constrained NMF algorithms.
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to comput…
We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based on projected gradient descent and the alternating direction method of multipliers. We prove that the se…
A new algorithm solves nonnegative least squares faster with nonnegative data.
problem Nonnegative least squares problems with nonnegative data.
method Primal-dual perspective accelerated algorithm with adaptive restart.
result Oracle complexity independent of matrix constants, solvable to multiplicative error.
BMM algorithm improves convergence for nonconvex optimization problems.
problem Constrained nonsmooth nonconvex optimization problems.
method Block majorization-minimization with diminishing radius.
result Improved convergence rate for nonconvex optimization problems.
New algorithm for nonnegative tensor completion with linear convergence rate.
problem Tensor completion without known optimal sample complexity rate.
method Integer optimization using a specific 0-1 polytope gauge norm.
result Achieves information-theoretic rate with linear convergence.
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute), some of which are further composed with linear maps. This kind of problems arises …
Unified approach for neural networks with multi-compartmental neurons and non-Hebbian plasticity.
problem Limited computational power of existing neural network models for multi-compartmental neurons and non-Hebbian plasticity.
method Unified extension of similarity matching approach to derive neural networks with multi-compartmental neurons and local, non-Hebbian learning rules.
result Unified approach facilitates understanding of multi-compartmental neuronal structures and non-Hebbian plasticity.
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first show that generic instances of the problem can be solved efficientl…
We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy has infinitely many path components. We also show that in each dimension there are at least homotopy s of pairwise distinct oriented diffeomorphism type for which the…
New method speeds up training of large kernel models.
problem Scaling kernel machines to large datasets and model sizes.
method Delayed projections in Preconditioned Stochastic Gradient Descent (PSGD).
result Significant training speed up over existing methods.
ZNMF improves facial recognition performance using data-dependent penalties.
problem Facial recognition performance in the Cambridge ORL database.
method ZNMF uses data-dependent auxiliary constraints to modify NMF.
result ZNMF outperforms other constrained NMF algorithms in facial recognition.
Paper speeds up tensor factorization algorithms.
problem Improving convergence speed of tensor factorization algorithms.
method Proposes an extrapolation strategy between block updates.
result HER significantly accelerates convergence speed.
We show that any closed biquotient with finite fundamental group admits metrics of positive Ricci curvature. Also, let M be a closed manifold on which a compact Lie group G acts with cohomogeneity one, and let L be a closed subgroup of G which acts freely on M. We show that the quotient N := M/L carries metrics of nonn…
Stochastic Earned Value Analysis using Monte Carlo Simulation and Statistical Learning Techniquesq-fin.RM
Paper introduces a new project control method using Monte Carlo and statistical learning.
problem Project control under uncertainty.
method Integrates Earned Value Methodology with Monte Carlo simulation and statistical learning.
result Estimates probabilities of project success and duration.
We demonstrate a new deep learning autoencoder network, trained by a nonnegativity constraint algorithm (NCAE), that learns features which show part-based representation of data. The learning algorithm is based on constraining negative weights. The performance of the algorithm is assessed based on decomposing data into…
Inspired by the advances in biological science, the study of sparse binary projection models has attracted considerable recent research attention. The models project dense input samples into a higher-dimensional space and output sparse binary data representations after the Winner-Take-All competition, subject to the co…